Question: Simplify; express your answer in exponential form. Assume $r\neq 0, n\neq 0$. $\dfrac{{(r^{-4}n^{-3})^{-5}}}{{(r^{-2}n^{-2})^{-2}}}$
Explanation: To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${(r^{-4}n^{-3})^{-5} = (r^{-4})^{-5}(n^{-3})^{-5}}$ On the left, we have ${r^{-4}}$ to the exponent ${-5}$ . Now ${-4 \times -5 = 20}$ , so ${(r^{-4})^{-5} = r^{20}}$ Apply the ideas above to simplify the equation. $\dfrac{{(r^{-4}n^{-3})^{-5}}}{{(r^{-2}n^{-2})^{-2}}} = \dfrac{{r^{20}n^{15}}}{{r^{4}n^{4}}}$ Break up the equation by variable and simplify. $\dfrac{{r^{20}n^{15}}}{{r^{4}n^{4}}} = \dfrac{{r^{20}}}{{r^{4}}} \cdot \dfrac{{n^{15}}}{{n^{4}}} = r^{{20} - {4}} \cdot n^{{15} - {4}} = r^{16}n^{11}$